Tropical quantum field theory and asymptotics of perturbation theory

Abstract: To compute properties of phase transitions in condensed matter or the interactions of elementary particles, quantum field theory is typically solved perturbatively. This expansion produces divergent series, so the extraction of meaningful results (resummation) is not straightforward. In fact, very little is known about the actual asymptotic behaviour of these series. In this talk, I will introduce a new limit of quantum field theory (the „tropical“ limit), which is easily computable to very high orders in perturbation theory, yet at the same time captures the full complexity of subdivergences, renormalization, and scheme dependence. I will illustrate that the values of Feynman integrals and their tropical limit are highly correlated. Based on data up to 400 loops, we can precisely determine the asymptotic growth of the (tropical) beta function in different renormalization schemes. In particular, we find unexpectedly complicated instantons, and we confirm the absence of renormalons in the minimal subtraction scheme.

mathematical physics

Audience: researchers in the topic

Seed Seminar of Mathematics and Physics

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